Identifying Place Values

What is the place value of each digit in $4.382$?

Identify the ones place: The digit before the decimal point is $4$ = $4$ is in the ones place (value: $4$)

Identify the tenths place: The first digit after the decimal is $3$ = $3$ is in the tenths place (value: $0.3$)

Identify the hundredths place: The second digit after the decimal is $8$ = $8$ is in the hundredths place (value: $0.08$)

Identify the thousandths place: The third digit after the decimal is $2$ = $2$ is in the thousandths place (value: $0.002$)

Answer: $4.382 = 4 + 0.3 + 0.08 + 0.002$

Finding the Value of a Digit

In the number $12.456$, what is the value of the digit $5$?

Locate the digit 5: Counting from the decimal point: 4 (tenths), 5 (hundredths) = $5$ is in the hundredths place

Determine the value: Hundredths means $\div 100$, so $5 \div 100 = 0.05$ = The value is $0.05$

Verify: $0.05$ means 5 hundredths or $\frac{5}{100}$ = Confirmed: value is $0.05$

Answer: The digit $5$ has a value of $0.05$ (five hundredths)

Comparing Decimal Place Values

Which digit has a greater value in $7.349$: the $3$ or the $9$?

Find the position of 3: $3$ is the first digit after the decimal = $3$ is in the tenths place (value: $0.3$)

Find the position of 9: $9$ is the third digit after the decimal = $9$ is in the thousandths place (value: $0.009$)

Compare the values: $0.3$ vs $0.009$: Which is larger? = $0.3 > 0.009$

Draw conclusion: Even though $9 > 3$ as digits, position matters more = The $3$ has a greater value

Answer: The digit $3$ (value $0.3$) is greater than the digit $9$ (value $0.009$) because it is in a higher place value position

Expanded Form of Decimals

Write $25.634$ in expanded form

Break down whole number part: $25 = 20 + 5$ = Tens: $20$, Ones: $5$

Identify the tenths: First digit after decimal is $6$ = Tenths: $0.6$

Identify the hundredths: Second digit after decimal is $3$ = Hundredths: $0.03$

Identify the thousandths: Third digit after decimal is $4$ = Thousandths: $0.004$

Write expanded form: Combine all place values = $20 + 5 + 0.6 + 0.03 + 0.004$

Answer: $25.634 = 20 + 5 + 0.6 + 0.03 + 0.004$

Mistake: Thinking $0.45$ is greater than $0.5$ because 45 > 5

Why: Students compare digits without considering place value. The 5 in $0.5$ is in the tenths place, while 45 represents 4 tenths and 5 hundredths.

Correct: Compare place by place: $0.5 = 0.50$, so $0.50 > 0.45$ because 5 tenths > 4 tenths.

Mistake: Reading $0.07$ as 'zero point seven' instead of 'zero point zero seven'

Why: The zero in the tenths place is important - it shows there are no tenths.

Correct: Read each digit: 'zero point zero seven' or 'seven hundredths.'

Mistake: Confusing tenths and tens, hundredths and hundreds

Why: The names sound similar but are on opposite sides of the decimal point.

Correct: Tenths ($0.1$) and hundredths ($0.01$) are fractions. Tens ($10$) and hundreds ($100$) are whole numbers.

Money and Shopping

Prices use decimal place values to show euros and cents.

A book costs 12.95 euros. The 9 is in the tenths place (9 ten-cent coins) and the 5 is in the hundredths place (5 cents).

Athletics and Sports

Race times are measured in seconds with decimal precision.

A swimmer finishes in 52.48 seconds. The 4 in the tenths place means 4 tenths of a second, and the 8 means 8 hundredths.

Measurements in Science

Scientists measure very precisely using many decimal places.

A pencil is 18.5 cm long. A feather weighs 0.003 kg (3 thousandths of a kilogram = 3 grams).

Q: Why do we need zeros in decimals like 0.05?

A: The zero shows there are no tenths. Without it, $0.5$ (five tenths) looks very different from $0.05$ (five hundredths). The zero is a placeholder that tells us exactly which place the 5 is in.

Q: Is 0.5 the same as 0.50?

A: Yes! Adding zeros to the right of a decimal doesn't change its value. $0.5 = 0.50 = 0.500$. They all equal five tenths or one half.

Q: How do I know which decimal is bigger?

A: Compare place by place from left to right. First compare tenths, then hundredths, then thousandths. The first place where the digits differ tells you which is larger.